Exploring complexity in a Schwarzschild radiating star

Abstract

We study the notion of complexity as defined by Herrera (L. Herrera, Phys. Rev. D 97, 044010 (2018) [1]) in a collapsing Schwarzschild-like star. Starting off with the static Schwarzschild interior solution cast in isotropic coordinates, we allow the mass function to be time-dependent. This gives rise to a dynamical radiating sphere with isotropic pressure and heat flux in the stellar interior. Since the star is radiating energy, the exterior spacetime is described by the Vaidya solution. The initial static solution described by the interior Schwarzschild solution is complexity-free. As hydrostatic equilibrium is lost and the configuration collapses, it enters a dynamical phase which is also complexity-free. We show that in order for the complexity to vanish, the density inhomogeneity is balanced by heat dissipation at each interior point of the stellar configuration.